A Mixed-Integer convex formulation for production optimization of gas-lifted oil fields with routing and pressure constraints

Abstract

-Production optimization of gas-lifted oil fields under facility, routing, and pressure constraints has attracted the attention of researchers and practitioners for its scientific challenges and economic impact. The available methods fall into one of two categories: nonlinear or piecewise-linear approaches. The nonlinear methods optimize simulation models directly or use surrogates obtained by curve fitting. The piecewise-linear methods represent the nonlinear functions using a convex combination of sample points, thereby generating a Mixed-Integer Linear Programming (MILP) problem. The nonlinear methods rely on compact models, but can get stuck in local minima, whereas the piecewise-linear methods can reach globally optimal solutions, but their models tend to get very large. This work combines these methods, whereby piecewise-linear models are used to approximate production functions, which are then composed with convex-quadratic models that approximate pressure drops. The end result is a Mixed-Integer Convex Programming (MICP) problem which is more compact than the MILP model and for which globally optimal solutions can be reached.

Optimal Shipping Route under the Designation of the Mediterranean Sulfur Emission Control Area: Mathematical Models and Applications

“…Furthermore, Camponogara et al [40] used a similar piecewise linearization approach to embed a well-fluid flow splitting model into an MILP formulation for production optimization. This technique has found widespread application in some publications [41,42]. We discretize the value of the objective function by ∆.…”

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“…Recent works have proposed alternate approximations. For instance, Aguiar et al used convex quadratic functions for pressure drops but multidimensional piecewise‐linear functions for well production to achieve global solutions. On the other hand, Grimstad et al used B‐spline based surrogates.…”

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“…While Kolb et al (2007) describe how gas network optimisation can be better achieved by developing piece-wise linear approximations of network components. In Camponogara et al (2011) and Aguiar et al (2014) gas-lifted oil field production costs are optimised by combining convex nonlinear regression curves with piece-wise linear approximations of these curves at given pressure and routing constraints. While Domschke et al (2011) solve a complex natural gas network optimisation problem by integrating piece-wise linear approximations to partially linearise a nonlinear cost function.…”